Classification of Stationary Points/Function of One Variable

Theorem

Let $f$ be a real function which is differentiable on the open interval $\openint a b$.

Let $P$ be a stationary point of $f$.

Then $P$ is either:

a local maximum

a local minimum

a point of inflection.

Proof

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Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): stationary point (critical point): 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): stationary point (critical point): 1.